Find the divergence of the function

[rude man]

Hmm Bp/p isn't a derivative I am failing to see what I can do with this. I am going to go on a long shot here and guess that the unit vectors cancel as they multiply together, and p cancels the other p and leaves me with z^2 again? Then z^2+z^2 heh that can't be right, what am doing wrong anymore hints?

B = B_ρ U_ρ + ...
= ρz² U_ρ + ...

div B = ∂B_ρ/∂ρ + B_ρ/ρ + ...
= z² + ρz²/ρ = z² + z² = 2z²

So you got it right, although I don't know exactly what you meant to say. You can see that the
ρ in the numerator and denominator of the second term do cancel.

 

[DODGEVIPER13]

ok will the rest of the terms work like this too?

 

[rude man]

ok will the rest of the terms work like this too?

You need to look up the general formula for the divergence in cylindrical coordinates. Then perform the indicated math.

Same goes for your C vector which is in spherical coordinates. You need to practice translating those general formulas into the specific expressions corresponding to your A, B and C.

It so happens that the B_ρ component of div B is the only one that has a non-derivative term in it. This is true only for cylindrical coordinates.

When you get to taking the curl you need to be comfortable in using Cramer's rule to solve the appropriate determinant.

 

[DODGEVIPER13]

ok my work is uploaded.